Problem: Solve for $x$ and $y$ using elimination. ${-x+5y = 5}$ ${x-4y = -3}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-x+5y = 5}\thinspace$ to find $x$ ${-x + 5}{(2)}{= 5}$ $-x+10 = 5$ $-x+10{-10} = 5{-10}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 2}$ into $\thinspace {x-4y = -3}\thinspace$ and get the same answer for $x$ : ${x - 4}{(2)}{= -3}$ ${x = 5}$